V alone can complete a piece of work in 10 days while W alone can complete the same piece of work in 15 days. To complete the work in 4 days, Z is hired. The money assigned for completion of work is Rs.900. how much money does Z earn from working on the project?

Correct option is B

Let the total work be represented by 1 unit of work.
- V can complete the work in 10 days. Therefore, V’s rate of work is:
Rate of V = 1/10 units per day.
- W can complete the work in 15 days. Therefore, W’s rate of work is:
Rate of W = 1/15 units per day.
Now, they are hired to complete the work in 4 days. Let Z’s rate of work be r_z, where r_z is the amount of work Z completes per day.
The total amount of work done by V, W, and Z in 4 days must equal the total work (1 unit):
​$$4 \times \left( \frac{1}{10} + \frac{1}{15} + r_z \right) = 1$$​​
First, calculate the combined rate of V and W:
$$\left( \frac{1}{10} + \frac{1}{15} + r_z \right) = \frac{1}{4}$$​​
First, calculate the combined rate of V and W:

$$\frac{1}{10} + \frac{1}{15} = \frac{5}{30}$$​​

Now, substitute this into the equation:

$$(5/30 + r_z) = 1/4$$​​
Solve for r_z:

$$1/6 + r_z = 1/4$$

$$r_z = 1/4 – 1/6 = 1/12$$​​
Thus, Z’s rate of work is 1/60 units per day. Since Z works for 4 days, the total work done by Z is:
Work done by $$Z = 4 (1/12) = 1/3$$​
Therefore, Z's earnings are proportional to the work done by Z:
Z's earnings = (1/3) x 900 = Rs 300​​